The close contact between Minoan men and Native American women, not surprisingly, appears to have resulted in the mixing of genetic material.

Yes, most characteristically including the conversion of Y-chromosomes into mitochondria.

http://www.chapelboro.com/Bronze-Age-Part-II–The-Case-of-the-Missing-Copper/9686450?pid=247221

One also wonders if this second migration was how Haplogroup X got into North America, which is only found in North America, and more dominant in the northern reaches than the South.

re: mtDNA X in the Americas, you may be interested to see my compilation of records from the literature here.

From what I have read, the only Asian population known to have it is the Altai, who have the same variant as native North Americans.

Actually, neither of the two American Indian subclades of X (X2a and the Ojibwa singleton X2g) have so far been detected anywhere in Eurasia. Reidla et al. (2003) established that the Altaian sequences all belong to X2e and suggested recent acquisition from the southern Caucasus. They also remarked on some new finds in Evenks:

In contrast to the Altaians, the Evenks did not harbor any West Eurasian mtDNA haplogroups other than X. However, neither of the two Evenk X haplotypes showed mutations characteristic of the Native American clade X2a. Instead, one sequence was a member of X2b and the other of X2*.

So the waters remain murky.

Reich and company are aware of the Yeniseian hypothesis but their analyses didn’t reveal any particularly pronounced connection between Kets and Na-Dene (or any other Native pops). But then again, the n for Kets was very low and (as Wade relates in the NYC) the presently available samples may be unrepresentative due to admixture (I guess with other Siberian pops? I don’t think they seemed especially Russian)

Given from what I have read, the first wave is estimated to have sprung from a very low population base (anywhere from low hundreds to dozens), I don’t know how you’d end retain a linguistically diverse population. In all historical situations where a mixed-language group comes into formation, the population becomes monolingual within a generation, with either the language of most prestige winning wholesale, or (in groups more isolated) an entirely new creole language forming.

I can believe that 15,000 years is too old for Amerind to be proven linguistically, but ultimately the languages need to have common antecedents, and those are most likely (barring anything like say an introduction of multiple language families by elite dominance by Eurasian/Australian groups who left no genetic record) going to be found within the Americas, or Beringia at worst.

IIRC, genetics has suggested the Selkup are an admixture of a Yenisian substratum and a Uralic group, so genetic links should be found there as well. Certainly Haplogroup Q of of Y-DNA is present in both Yenisians and Selkups, but it is also hugely prevalent throughout the Americas – and actually depressed in the north – which would argue against a linkage.

One also wonders if this second migration was how Haplogroup X got into North America, which is only found in North America, and more dominant in the northern reaches than the South. From what I have read, the only Asian population known to have it is the Altai, who have the same variant as native North Americans. Oddly, other Turkic populations in central Asia lack X, suggesting it was a holdover from an indigenous population which underwent language shift. This is particularly the case because any expansion into North America must have happened well before the Turkic expansion.

The Y-DNA haplogroup C3b is also interesting. AFAIK, not a lot of Na-Dene populations have been tested for it, but it has a higher frequency in the interior western Canada, and is fairly prevalent among the Apache (15%). In general it seems like from this study that some Algonquin populations received some admixture from whatever population source birthed the Na Dene, so high frequency in groups like the Cheyenne might be evidence as well.

Of course, the lack of prevalence of both these rarer Y-DNA and mt-DNA groups further south could in part just be due to the aforementioned genetic bottlenecks. Still, it’s intriguing. Hopefully with the growth of personal genomics in the U.S., more Native American genomes from the USA will be studied soon.